If $\tan {25}^{\circ }=x,$ then, $\mathrm{then} \frac{\tan {155}^{\circ }-\tan {115}^{\circ }}{1+\tan {155}^{\circ }\tan {115}^{\circ }}$is equal is 

$\frac{\tan {155}^{\circ }-\tan {115}^{\circ }}{1+\tan {155}^{\circ }\tan {115}^{\circ }}$

$=\frac{\tan \left({180}^{\circ }-{25}^{\circ }\right)-\tan \left({90}^{\circ }+{25}^{\circ }\right)}{1+\tan \left({180}^{\circ }-{25}^{\circ }\right)\tan \left({90}^{\circ }+{25}^{\circ }\right)}$

$=\frac{-\tan {25}^{\circ }+\cot {25}^{\circ }}{1+\tan {25}^{\circ }\cot {25}^{\circ }}=\frac{1}{2}\left(-x+\frac{1}{x}\right)=\frac{1-x^2}{2x}$